Lab Activity :Digital Communication Systems - Due in 24 hours

ECE4513 Digital Communication Systems Laboratory

Dennis Silage, PhD [email protected]

BER of Bi-Phase-L with Optimum Receiver v2

The performance of a digital communication system in the presence of additive white Gaussian noise (AWGN) can be assessed by the measurement of the bit error rate (BER). The bi-phase (Manchester or sometimes also called split phase RZ) line code is to be used here. MS Figure 4.20 contains the bi-phase-L (or split phase RZ) baseband transmit signal generator (lower right) and three other signals which can be simplified and used here. The bi-phase-L (or split phase RZ) signal is shown in MS Figure 4.21 with an output amplitude of ±1 for the binary bit stream 111001001….

MS Figure 4.20 AMI NRZ and RZ and split-phase RZ line code binary data generators (Fig420.slx).

Bi-phase-L is a symmetrical baseband signal. The binary rectangular symmetrical pulse amplitude modulated (PAM) NRZ digital communication system with BER analysis and the optimum correlation receiver is shown in MS Figure 2.34. This model forms the basis for the bi-phase-L digital communication system to be designed by you here. The optimum correlation receiver reference signal in MS Figure 2.34 is a rectangular pulse with a near 100% duty cycle or a constant value. The reference signal and the receiver structure must be altered here to accommodate the bi-

phase-L (or split-phase RZ) signal. A single correlation function receive structure is to be used.

MS Figure 4.21 Split Phase RZ (Bi-Phase-L)

MS Figure 2.34. A binary rectangular symmetrical PAM digital communication system with BER analysis and the optimum correlation receiver (Fig234.slx).

In the Simulink model Fig234.slx the parameters of the Random Integer Generator block data source and the rectangular PAM transmitter is a rate of rb = 1 kb/sec, M = 2 levels (binary) and a resulting amplitude of 0 and 1 V. The transmitter offset (TX offset) and gain (TX Gain) of 10 implies that the transmitted pulse is ± 5 V. Your task is to modify this Simulink model Fig234.slx with new parameters and reconfigured transmitter and receiver. The bi-phase-L (or split phase RZ) baseband transmit signal generator from a portion of MS Figure 4.20 replaces the binary rectangular PAM signal generator of MS Figure 2.34. Your transmitter design will utilize baseband amplitudes of ±Vs and a data rate rb b/sec derived from the transmitter gain (TX Gain) and bit time Tb assigned to you: The transmitter gain (TX Gain, 5 in the Simulink model) = [sum of the 2nd through 4th digits of your TU ID]/10

The bit time (Tb = 1 msec in the Simulink model) = [sum of the 3rd, 4th, and 6th digits of your TU ID] as milliseconds (msec) In this Laboratory you are to assess the BER performance of the Bi-phase-L baseband signal with an optimum receiver. You must choose an appropriate simulation step time TS. This data rate is somewhat higher than the Simulink model in MS Figure 2.34 (1 kb/sec) which used a 20 µsec simulation step time TS or a simulation frequency fS = 1/ TS = 50 kHz resulting in 50 sample points per bit time, which is a reasonable simulation resolution. Therefore the simulation step time TS = 1/ fS and the parameters of the Data Rate Translation blocks, the receiver correlation reference Pulse Generator blocks, the Integrate and Dump block, the optimal threshold values for the receiver binary data detection and the delay between the transmitted and received bits in the Error Rate Calculation block must all be carefully chosen for the simulation in this Laboratory to be correct. Obtaining 0 BER with no AWGN for each of the Laboratory simulations is crucial since all other reported measurements will be incorrect if this is not met. If a non- zero BER with no AWGN is obtained, timing parameters and delays are the usual problems that can cause this performance error and could be different in each of the simulations specified. The Laboratory tasks are as follows:

1. Run the simulation of the binary rectangular symmetrical PAM NRZ Simulink model Fig234.slx with the standard model parameters to familiarize yourself with the BER analysis before starting your project. MS Table 2.8 shows the observed and theoretical BER performance for fixed steps in the value of Eb/No for a sequence of 10 000 random, equally likely data bits for a binary rectangular symmetrical PAM binary data signal.

2. Configure a single correlator receiver in a Simulink simulation with a

receiver reference source that you will develop as φ2^(t). Note that the NS text has the signals as s2(t) (binary 1) and s0(t) (binary 0). Show the determination of φ2^(t) and its implementation as a signal source. Plot the signal for several bit times in Simulink to verify its performance.

Scaling of the single correlator by the denominator term of φ2^(t) is not required because of the Simulink Sign block in the receiver structure. The threshold T = 0 since the bi-phase-L (or split phase RZ) baseband signal is symmetrical and with equally likely binary data with P1 = P2.

3. Configure the single correlator receiver with this receiver reference source φ2^(t) as shown below. The Simulink model Fig234.slx is a rectangular symmetrical pulse amplitude modulated (PAM) binary baseband digital communication system with an AWGN channel and the optimum correlation receiver and provides a template here.

4. Calculate the power in your bi-phase-L transmitted signal assuming equally likely binary data and compute the SNR in dB in the standard range ∞, 10, 8, 6, 4, 2 and 0 dB by first determining Eb then setting the AWGN channel appropriately. Here use the Eb/No ratio for the noise generated by the AWGN channel as described in the MS text and not the noise variance σ2.

2 2

( -1)

s ( ) d ( 1) 0,1= −   = b

b

iT

j

b j b b

i T

E γ t t i T t iT j MS Eq. 2.28

j 0 1b j b 0 b 1 b j

P P P P P P P= = + MS Eq. 2.30

5. Run your simulation for your bi-phase-L binary data signal. Does your

implementation of the bi-phase-L binary system in AWGN produces similar BER tabular results as in MS Table 2.8 using the theoretical probability of bit error Pb for a symmetrical binary signal and the energy per bit Eb shown below? Note that it is not reasonable in digital communications to even report a BER greater than approximately 0.1 (1 in 10 bits in error).

2 Q bb

o

E P

N

  =   

  MS Eq. 2.31

6. Produce a table of your BER for the bi-phase-L digital communication system and compare that to MS Table 2.8 for a binary symmetrical rectangular PAM binary data signal. Comment on any apparent differences.

This Laboratory is for the two weeks starting October 1st and October 8th and due no later than Wednesday October 17th at 11:59 PM. You will be required to demonstrate all Laboratories during the semester, so your Model and Laboratory Report should be maintained.

Fall 2018